2026-07-24T14:56:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:10502 2024-03-06T10:45:54Z ddc:004 open_access

Searching Long Repeats in Streams Merkurev, Oleg Shur, Arseny M. Longest repeated substring longest repeated reversed substring streaming algorithm Karp Rabin fingerprint suffix tree We consider two well-known related problems: Longest Repeated Substring (LRS) and Longest Repeated Reversed Substring (LRRS). Their streaming versions cannot be solved exactly; we show that only approximate solutions by Monte Carlo algorithms are possible, and prove a lower bound on consumed memory. For both problems, we present purely linear-time Monte Carlo algorithms working in O(E + n/E) space, where E is the additive approximation error. Within the same space bounds, we then present nearly real-time solutions, which require O(log n) time per symbol and O(n + n/E log n) time overall. The working space exactly matches the lower bound whenever E=O(n^{0.5}) and the size of the alphabet is Omega(n^{0.01}). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Oleg Merkurev and Arseny M. Shur 2019 Is Part Of LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2019.31 urn:nbn:de:0030-drops-105029 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.31 eng https://creativecommons.org/licenses/by/3.0/legalcode